US9891344B2 - Computer estimation method, and method for oil exploration and development using such a method - Google Patents

Computer estimation method, and method for oil exploration and development using such a method Download PDF

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US9891344B2
US9891344B2 US14/004,052 US201214004052A US9891344B2 US 9891344 B2 US9891344 B2 US 9891344B2 US 201214004052 A US201214004052 A US 201214004052A US 9891344 B2 US9891344 B2 US 9891344B2
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Denis Allard
Alexandre Walgenwitz
Pierre Biver
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V11/00—Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
    • G01V11/002—Details, e.g. power supply systems for logging instruments, transmitting or recording data, specially adapted for well logging, also if the prospecting method is irrelevant
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V11/00—Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V20/00—Geomodelling in general
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V99/00—Subject matter not provided for in other groups of this subclass
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/66—Subsurface modeling
    • G01V2210/665—Subsurface modeling using geostatistical modeling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Definitions

  • the present invention relates to computer methods of estimation, methods of oil exploration and exploitation implementing such methods.
  • the invention pertains to a computer method for estimating a suite of quantities associated with locations of a space, for example a method for modeling petrophysical quantities of a reservoir or a method for mapping the depth or thickness of a geological layer.
  • interpolation methods such as kriging.
  • Kriging is an unbiased interpolator which minimizes the mean square prediction error and which makes it possible to honor the available data (it is an exact interpolator).
  • a difficulty related to kriging is that it requires large computational power to invert the covariance matrix. This is true in particular when working on a large space, using numerous observation data.
  • the aim of the present invention is in particular to alleviate these drawbacks.
  • a computerized method for estimating a suite of quantities associated with locations of a space comprising the following steps:
  • a quantity associated with at least one location of a first sub-space included in said space is estimated by kriging, using the precision matrix of the first sub-space,
  • a quantity associated with at least one location of the second sub-space is estimated by kriging on the basis of the first sub-space, of the second sub-space, and of the precision matrix determined for the first sub-space.
  • the precision matrix is the inverse of the covariance matrix.
  • A denotes the set of locations of the first sub-space
  • C X,Y denotes the covariance matrix of the sets X and Y
  • ⁇ 1 denotes the matrix inversion operation
  • A denotes the set of locations of the second sub-space
  • C X,Y denotes the covariance matrix of the sets X and Y
  • ⁇ 1 denotes the matrix inversion operation
  • the invention pertains to the hydrocarbon produced by such a method.
  • the invention pertains to the computer program product suitable for implementing the steps of such methods when it is implemented on a programmable machine.
  • FIG. 1 is a cross-sectional schematic view of a space
  • FIG. 2 is a schematic view from above of data of observations obtained in the space
  • FIG. 3 is a schematic view of a method for searching for neighboring sub-spaces
  • FIG. 4 is a schematic view of a kd-tree
  • FIG. 5 is a schematic view from above of a set of quantities estimated by an embodiment of the method
  • FIG. 6 is a descriptive flowchart of an exemplary embodiment of the method.
  • FIG. 7 is a schematic view of a computing system suitable for implementing the method.
  • FIG. 1 schematically represents a section of a space 1 whose oil-bearing character it is desired to estimate.
  • the space studied may for example be two-dimensional, such as the plane represented, or three-dimensional, comprising a large number of such sections distributed along the direction normal to the cross-sectional plane of FIG. 1 .
  • Z is the vertical direction
  • X the horizontal direction included in the p14229ane.
  • the space studied is for example a subsurface for which it is envisaged that oil exploitation be undertaken. For this purpose, it is possible to seek to determine a certain number of quantities characteristic of the subsurface.
  • the quantities that it is sought to estimate are quantities typical of a hydrocarbon reservoir such as the thicknesses of geological layers disposed in the subsurface, the presence and the amount of fluids, hydrocarbons, the net-to-gross (NG), the fluid velocities, the porosity, the net sand, etc. and combinations of these quantities, in particular, any quantity making it possible to model a hydrocarbon reservoir in the space considered.
  • quantities typical of a hydrocarbon reservoir such as the thicknesses of geological layers disposed in the subsurface, the presence and the amount of fluids, hydrocarbons, the net-to-gross (NG), the fluid velocities, the porosity, the net sand, etc. and combinations of these quantities, in particular, any quantity making it possible to model a hydrocarbon reservoir in the space considered.
  • FIG. 2 represents, at a certain number of locations 2 a , 2 b , 2 c the value of the measured quantity for this location.
  • the locations represented in light gray, such as the location 2 a show that the quantity measured here is higher than a certain higher threshold.
  • the locations, such as the location 2 c represented in dark gray, the measured value of the quantity is lower than a certain lower threshold.
  • the locations, such as the location 2 b symbolized in white in FIG. 2 , the value measured for the quantity lies between the above-mentioned two thresholds. Measurements of value of the quantity are thus obtained at a restricted number of locations of the space, the value of the quantity in the other locations being unknown.
  • observation data 2 a , 2 b , 2 c are obtained by seismic imaging of the subsurface.
  • the locations for which the quantity is measured may exhibit very disparate spacings. For example, in FIG. 2 , they may be spaced apart by the order of several meters to several kilometers.
  • step 102 a location x 0 for which it is desired to estimate the quantity Z(x 0 ) is determined
  • the point x 0 is represented by an upward pointing triangle in FIG. 3 .
  • the locations S i are represented by crosses in this figure.
  • a neighborhood V(x 0 ) of the location x 0 is determined This neighborhood consists for example of a set of n 0 locations S i for which a measurement of the quantity is available, and situated preferably a distance of less than a predetermined threshold from the location x 0 .
  • the distance in question can be any distance suitable for the situation, such as the Manhattan and Euclidian distance, or some other distance.
  • the number n 0 can be for example sixteen locations Si, two hundred locations Si, or some other number.
  • step 104 the value of the quantity Z k (x 0 ) at the point x 0 is then estimated by kriging.
  • kriging denotes an unbiased linear spatial forecaster obtained by minimizing the prediction variance, it being assumed that the covariance function of the quantity Z is known.
  • C is the n ⁇ n covariance matrix whose elements are C(s ⁇ ⁇ s ⁇ ) and where C(h) is the covariance function of the quantity Z, ⁇ is the vector of the n weightings ⁇ ⁇ , and C 0 is the vector of elements C(s 0 ⁇ s ⁇ ).
  • the matrix C is symmetric, definite, positive and invertible.
  • covariance function use is made of any appropriate covariance function such as the exponential covariance function, square exponential function, or any other admissible covariance function.
  • Recourse is not necessarily had to simple kriging. Recourse may as a variant be had to another type of kriging such as ordinary kriging, universal kriging, kriging with external drift.
  • step 105 a location x i near to x 0 is determined The location x 1 is indicated by an downward oriented triangle in FIG. 3 .
  • the location x 1 is determined as a function of the location X 0 in any appropriate way, such as, for example, the location nearest to X 0 for which no value has yet been estimated for the quantity.
  • step 106 the neighborhood V (X 1 ) of the locations near to X 1 for which a measured value for the quantity is available is determined.
  • the neighborhood V (X 1 ) is represented delimited by a dashed line in FIG. 3 .
  • the set of points S i forming part of the neighborhood V(X 1 ) and of those forming part of the neighborhood V (X 0 ) are identical.
  • step 108 it is determined whether an estimation of the values of the quantity has been obtained for sufficient spacings. If such is not the case, step 106 is returned to while incrementing the index i of the location for which the value of the quantity is estimated in step 109 .
  • the neighborhood V(X i ⁇ 1 ) of a point X i will end up being different from the neighborhood V(X i ⁇ 1 ) for the previous location X i ⁇ 1 . That is to say the method operates by sliding of the neighborhood.
  • the location X 2 is represented by a rightward oriented triangle, and the neighborhood V (X 2 ) by a chain dotted line.
  • the neighborhood V (x 2 ) is distinguished from the neighborhood V (X 1 ) by the addition of locations identified S + and by the removal of locations identified S.
  • the second sub-space is obtained by adding locations to the first sub-space.
  • A is V(s 1 ), the neighborhood of s 1 ), for which the covariance matrix C A,A , of dimension N ⁇ N is known. This matrix has already been inverted, and its inverse, C ⁇ 1 A,A , has been stored.
  • the conventional expedient would have consisted in creating the matrix
  • a ⁇ U _ ⁇ B ( C A , A C A , B C A , B t C B , B ) ,
  • the algorithm is fast, already knowing C A,A ⁇ 1 :
  • the number of operations required to carry out this inversion is of the order of n 3 +2(N 2 n+n 2 N), that is to say that of the order of N 2 operations remain. This is a considerable time saving.
  • the second sub-space is obtained by deleting locations from the first sub-space.
  • the locations s are the locations to be removed. It is assumed here that these sites relate to the last rows and columns of the matrix. We therefore have a matrix:
  • step 107 the value of the quantity at s 2 is estimated by kriging.
  • the method is looped until the estimation has been obtained for the set of desired locations (end step 110 ), for example some thousands of locations.
  • the method therefore makes it possible to work with large neighborhoods, by updating the precision matrix (inverse of the covariance matrix) according to the above equations.
  • Working with a large neighborhood exhibits several advantages:
  • the precision matrix is maintained so that the sites are arranged in order of their increasing distance from the estimation site. This is done for the following reasons:
  • the updating of the matrix therefore entails the following steps:
  • FIG. 5 An exemplary representation of the results arising from the method described above is given in FIG. 5 .
  • the latter corresponds to the result of the simulation method implemented on the basis of the observation data represented in FIG. 2 , and the same color code applies to this figure.
  • the zones 2 a ′, 2 b ′, 2 c ′ are thus recognized, corresponding respectively to the zones 2 a , 2 b , 2 c of FIG. 2 .
  • Tests carried out on one and the same computing system make it possible for the result represented in FIG. 5 to be obtained in 10 minutes, whereas about 120 minutes are required to obtain a similar result for a conventional method.
  • the conventional method moreover involves only 16 locations in the neighborhood, whereas, during this trial, the present method has been implemented with 200 locations in the neighborhood. The result obtained is therefore more precise for a comparable computational power.
  • One of the steps of the invention consists in determining a neighborhood of location of the point considered where the value of the quantity is to be estimated.
  • An exemplary method for the construction of such a neighborhood involves Kd-trees 3 such as represented in FIG. 4 .
  • the tree-like structure used is a binary tree in which each node represents at one and the same time a subset of the given locations and a partitioning of this subset.
  • the root node 3 0 represents the entirety of the given locations.
  • Each non-terminal node 3 i possesses two child nodes 3 i+1 , 3 i+2 , which represent the two subsets defined by the partitioning.
  • the terminal nodes 3 z represent small mutually disjoint subsets which form a partition of the given locations.
  • the partitioning consists in determining on the associated locations the component of maximum variability, and then in choosing the median value of this component as separation limit.
  • the maximum number of locations for each non-terminal node is fixed at an arbitrary value nb.
  • each node of the tree there corresponds a domain of patch type encompassing the locations associated with this node, and whose limits are defined by the successive partitionings associated with the parent nodes.
  • the domain corresponding to the root node is the entire space.
  • the volume of the domain decreases according to the increasing level of depth in the tree.
  • the above tree of locations is therefore constructed in the course of an initial step, after having obtained the observation data.
  • the search algorithm uses a recursive sweep through the depth of the tree.
  • the recursive procedure considers the root node at the first call. If the node considered is terminal then all the associated locations are examined. A list of the k nearest neighbors encountered together with their dissimilarity at the enquiry location is maintained in the course of the search in the form of a priority queue. When an examined location is found nearer than the furthest location of this list, the list is updated. If the node considered is non-terminal, then the recursive procedure is called on the child node representing the locations situated on the same side of the partition as the enquiry location.
  • a test is performed to determine whether it is necessary to examine the locations situated on the opposite side of the partition from the enquiry location. The examination is necessary when the domain delimiting these locations intercepts the ball centered at the enquiry location and of radius equal to the dissimilarity of the k th current nearest neighbor. In the affirmative the recursive procedure is called on the child node representing these locations.
  • a test is performed to determine whether it is necessary to continue the search. Continuation is not necessary when the ball centered at the enquiry location and of radius equal to the dissimilarity of the k th current nearest neighbor is entirely contained in the domain associated with the node considered.
  • the above search algorithm is for example implemented in step 103 to determine the neighborhood of the location x 0 .
  • This method could be implemented to determine the neighborhood of each location.
  • An envisaged solution is to force the distribution of the nearest neighbors in all directions. In the case of an application to a three-dimensional domain, it is possible to force the distribution of the nearest neighbors as a function of the octants around the point to be kriged.
  • Taking octants into account consists in constraining the search for the nearest neighbors in accordance with each octant and then merging the searches. It is necessary to make one or more (one per octant) traversals of the tree.
  • the method therefore proceeds as follows to impose a distribution of the nearest neighbors:
  • the space is divided into S sectors.
  • the set of preselected nearest neighbors must be at least equal to V.
  • a simple way is to take a number N near to V. This number N will be able to depend upon the distribution of the measurements, the number of sectors, the points to be kriged, etc.
  • This method makes it possible to perform a sectorially distributed procedure for choosing. The selection is thereafter supplemented if sectors are deficient.
  • the distance used in the description hereinbelow is the Euclidian distance, or any other suitable distance.
  • a moving enquiry location is considered and its position is denoted x t .
  • D t (i) to be the distance of the i th nearest neighbor (among the locations s 1 , . . . , s n ) of x t and ⁇ t to be the initial search bound guaranteeing to find at least the k nearest neighbors of x t .
  • D t (k) ⁇ t .
  • the k nearest neighbors of the enquiry location at the position x t are ⁇ p 1 , p 2 , . . . , p k ⁇ and D t (k) is the maximum distance of these locations from x t .
  • ⁇ is the distance between x t and x t+i .
  • the set P of k nearest neighbors of the enquiry location at the position x t is P ⁇ p 1 , p 2 , . . . , p k ⁇ , D t (k) is the maximum distance of these locations from x t and D t (k+1) is the minimum distance of the locations outside of this set P from x t .
  • the enquiry location shifts to the position x t+1 . Then the neighborhood obtained is unchanged if ⁇ (1 ⁇ 2) (D t (k+1) ⁇ D t (k)), where ⁇ is the distance between x t and x t+1 .
  • the neighborhood obtained still contains the locations p i satisfying D t (i) ⁇ D t (k+1) ⁇ 2 ⁇
  • ⁇ is the distance between x t and x t+1 .
  • the m nearest neighbors of the enquiry location at the position x t are stored in a buffer, where m>k.
  • D t (k) and D t (m) are respectively the k th and m th distances associated with these locations.
  • the enquiry location shifts to the position x t+1 . Then it is not necessary to update the buffer if ⁇ (1 ⁇ 2) ( D t ( m ) ⁇ D t ( k )) where ⁇ is the distance between x t and x t+1 .
  • the first buffer is intended for the candidate locations for the current enquiry position.
  • the second buffer is intended for the candidate locations for the next enquiry position.
  • the initial search bound in this example is thus always lower than that in the method according to the first example.
  • the method which is described above for one quantity can be implemented for a suite of quantities comprising one or more quantities to be estimated.
  • the above method makes it possible to confirm the presence of hydrocarbons to be extracted from the zone considered, it is possible to construct an oil exploitation rig 4 for the space considered.
  • the grid obtained by the above method can be used to estimate the characteristics of the hydrocarbons field, and, consequently, to estimate the installation characteristics of the oil exploitation rig. This exploitation then makes it possible to extract hydrocarbons.
  • FIG. 7 describes an exemplary simulation device 600 .
  • the device comprises a computer 600 comprising reception means 601 designed to receive an observation of a given quantity for the geological region, such as for example a modem 601 linked to a network 605 , itself in communication with a device 606 providing observation data.
  • the device 600 furthermore comprises a memory for storing a mesh of the space studied.
  • Processing means for example a processor 602 , are suitable for implementing the above method on the basis of the observation data obtained and of the mesh stored in the memory.
  • the processing means 602 are for example able to execute steps 101 to 110 of FIG. 6 .

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FR1151911 2011-03-09
FR1151911A FR2972539B1 (fr) 2011-03-09 2011-03-09 Procede informatique d'estimation, procede d'exploration et d'exploitation petroliere mettant en oeuvre un tel procede
PCT/FR2012/050492 WO2012120241A1 (fr) 2011-03-09 2012-03-08 Procede informatique d'estimation, procede d'exploration et d'exploitation petroliere mettant en oeuvre un tel procede

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AU2013283825B2 (en) * 2012-06-26 2017-02-02 Total Sa Truncation diagram determination for a pluri-gaussian estimation
CA3035549C (fr) * 2016-11-04 2020-08-18 Landmark Graphics Corporation Determination de contraintes actives dans un reseau au a l'aide de pseudo-variables d'ecart

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GB2502918A (en) 2013-12-11
FR2972539A1 (fr) 2012-09-14
GB2502918B (en) 2016-08-03
WO2012120241A1 (fr) 2012-09-13
US20140149044A1 (en) 2014-05-29
NO346088B1 (no) 2022-02-07
NO20131328A1 (no) 2013-10-03
GB201315670D0 (en) 2013-10-16

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